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1 Force versus distance graph Objectives Investigate examples of kinetic and potential energy and their transformations. Calculate work from the area under the force vs. distance graph. Relate the net work done on an object to its change in kinetic energy. Demonstrate the use of course apparatus and equipment, including slotted or hooked masses, spring scales, meter sticks, graph paper, graphing technology, and data acquisition probes. work on the system, what type of energy does the system have, and 3. AFTER the elastic band does work on the system, what type of energy does the system have, and Physics terms force work force vs. distance graph Equations Work done by a constant force: Area of a rectangle: Area of a triangle: 1

2 If the object moves 2 meters, how much work is done? The work done by a force equals the force times the distance moved in the direction of the force. If the object moves 2 meters, how much work is done? Reading the graph A graph of force vs. distance for this event is shown. The object moves 2 meters. The work done equals the area of the shaded rectangle. The work done equals the area under the force vs. distance graph. If the force is constant, this area is a rectangle. But what if the force is not constant? 2

3 The force shown here is NOT constant. The work done equals the triangular shaded area. How do we find the work done in this example? In 9A on the force vs. distance graph you will explore the relationship between work and energy. The investigation is found on page 262. Gather your materials. Calibrate the spring scale if needed. 1. Stretch the elastic band to different distances and measure the force with a spring scale. Tabulate your results. 2. Using your computer, click on the graphing tool in the electronic resources to conduct the investigation. Plot force versus the displacement of the band. Calculate the elastic potential energy at each displacement. 3. For each displacement, release the ErgoBot and capture its motion data on the computer. Record the maximum speed and calculate the kinetic energy. Add these values to your table. 3

4 Questions for Part 1 a. How does the work done by the elastic band compare with the E k of the ErgoBot? Why? b. What are the independent, dependent, and controlled variables? Gather your materials. Select a hanging mass that allows for a brisk but controlled acceleration. 1. Release the suspended mass and capture the motion data on the computer. 2. For at least 5 points on the motion graph, determine the distance traveled and the acceleration. 3. Calculate the net force at each distance by applying Newton s second law: F net = ma. 4. Plot a graph of force vs. distance for the ErgoBot. Questions for Part 2 a. Use the motion graphs to determine v max at the end of the accelerated motion. What was the maximum E k? b. Calculate the total work done on the ErgoBot from the area under the graph of force vs. distance. c. How does the total work done on the ErgoBot compare with its maximum kinetic energy? 4

5 much? elastic potential energy = 4 J much? elastic potential energy = 4 J much? kinetic energy = 4 J 5

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